Advanced Linear Modeling

Now in its third edition, this companion volume to Ronald Christensen’s Plane Answers to Complex Questions uses three fundamental concepts from standard linear model theory—best linear prediction, projections, and Mahalanobis distance— to extend standard linear modeling into the realms of Statistical Learning and Dependent Data. This new edition features a wealth of new and revised content. In Statistical Learning it delves into nonparametric regression, penalized estimation (regularization), reproducing kernel Hilbert spaces, the kernel trick, and support vector machines. For Dependent Data it uses linear model theory to examine general linear models, linear mixed models, time series, spatial data, (generalized) multivariate linear models, discrimination, and dimension reduction. While numerous references to Plane Answers are made throughout the volume, Advanced Linear Modeling can be used on its own given a solid background in linear models. Accompanying R code for the analyses is available online.

1. Nonparametric Regression.- 2. Penalized Estimation.- 3. Reproducing Kernel Hilbert Spaces.- 4. Covariance Parameter Estimation.- 5. Mixed Models and Variance Components.- 6. Frequency Analysis of Time Series.- 7. Time Domain Analysis.- 8. Linear Models for Spacial Data: Kriging.- 9. Multivariate Linear Models: General. 10. Multivariate Linear Models: Applications.- 11. Generalized Multivariate Linear Models and Longitudinal Data.- 12. Discrimination and Allocation.- 13. Binary Discrimination and Regression.- 14. Principal Components, Classical Multidimensional Scaling, and Factor Analysis.- A Mathematical Background.- B Best Linear Predictors.- C Residual Maximum Likelihood.- Index.- Author Index.